“Longhorn” is the nickname of the University of Texas (Austin) teams. The term was officially and regularly used in 1906.
 
It had been written that “Longhorns” was used in the Daily Texan newspaper from 1903, but “Long Horns” was used in 1900 newspaper articles.
 
 
Mack Brown Texas Football: “The Texas Longhorn”
The Texas Longhorn
Bevo, a Texas longhorn, has been a fixture at UT games since 1966. The longhorn mascot epitomizes the pride and tradition of Texas Football.
The longhorn was an important part of the building of the American West. Brought to the North American continent by Spanish explorers, the breed has flourished for almost 500 years.

With its roots on the hot, arid plains of South Texas, the longhorn became a major food source for young America. First it survived with little grass and food to eat. In a world vulnerable to attack, its long horns and strong legs became effective weapons against wild animals looking for prey.

When the railroad made places such as Omaha and Kansas City chief stops for a nation moving west, cattlemen used the famed Chisolm Trail to drive their cattle to market. The 1,000-mile trek would take months, but while other breeds couldn’t make it because of the long odds, the lean, mean longhorn survived.

Independent, never tame, and always on guard, longhorns grow to a ton or more, and the span of the great horns can reach six to nine feet. In the early 1900s, when The University of Texas was looking for a mascot, none fit better for the young college than the longhorn — a breed apart because of its toughness and strength, determination to survive, and will to win against all odds.
   
Mack Brown Texas Football: “History of Texas Football”
The History of Texas Football
by Bill Little (with special thanks to Lou Maysel, author of “Here Comes the Texas Longhorns,” Vols. I&II)
(...)
By the turn of the century, football was still a crude, rough game of bullish runs up the middle, but it had caught on at the Austin campus. A muddle over school colors was settled when, on May 10, 1900, the Board of Regents officially declared them to be orange and white. The first band was organized in 1900 as well. The initial instruments were purchased from a local pawn shop, and the brass horns had to be taken to a tin shop for soldering before they could be used.
 
In 1903, a Daily Texan writer, D. A. Frank, first labeled the team, “The Longhorns,” and the name eventually stuck after constant usage.
 
Texas Longhorn Traditions
Alex Weisburg, editor-in-chief of the Daily Texan in 1903, told his staff to refer to every University sports team as “The Longhorns” and they’d soon have it named. These instructions were followed and passed down for several years, and around 1906, the name became official!
   
18 November 1900, Galveston Daily News, “Football Game at Austin,” pg. 2:
Austin, Tex., Nov. 17.—Texas to-day avenged former defeats, and the long horns clipped the Tigers’ claws by a score of 17 to 11 in one of the most exciting games played in this city.
   
25 November 1900, Daily Express (San Antonio, TX), pg. 7:
LONG HORNS
THE CHAMPIONS
 
TEXAS VARSITY ARE NOW FOOTBALL
LEADERS IN THE SOUTHWEST.   
 
11 October 1902, Dallas Morning News, pg. 3:
WON BY VARSITY
 
SEWANEE MEN UNABLE TO WITH-
STAND PONDEROUS ASSAULTS
OF TEXAS ELEVEN.
(...)
Heavyweight Longhorns Go Through
and Around Tennessee Oppo-
nent’s Line with Ease.
(...)
There were so many persons who wore the colors of the Tennessee men that their number seemed almost, if not quite, equal to those who were straining their lungs and rasping their throats with cheers for the Texas warriors.
 
Rattle de thrat, de thrat,
Rattle de thrat, de thrat,
Long horns! Cactus thorns!
Texas! Texas! Texas!
Ugh-h-h-h!”
 
10 November 1905, Dallas Morning News, “Kentucky Team in Austin,” pg. 12:
The Blue Grass team is heavier than Texas and has a long string of hard-earned victories to its credit, but the long horns from Texas are fighters and will be hard to down, if at all.
 
2 October 1906, Dallas Morning News, pg. 11:
In the past the Texas team has been handicapped by playing strong teams early in the season, but Manager Lumpkin has arranged better dates and the best guarantees ever given to Texas athletes. The Haskell Indians, one of the strongest teams in the West, will be met late instead of early, as heretofore, and Texas may finally win a victory, as the longhorns were not in condition on former occasions, yet the Indians barely scratched out with the ribbon.
 
24 November 1906, Galveston (TX) Daily News, pg. 4:
At the end of the first half the score was against Texas by one point, and soon after the whistle blew for the second start the Longhorns walked away from the Missourians.